$$\begin{bmatrix} 111 & 100 & 225 & 235\\ 220 & 312 & 220 & 410\\ 215 & 180 & 268 & 305\\ 315 & 145 & 205 & 122 \end{bmatrix}$$
Guys is it enough to show that after Gaussian elimination whether we get lower/upper triangle we also get non zero diagonal entries ($a_{11}$,$a_{22}$,$a_{33}$,$a_{44}$), therefore determinant is the multiplication of these entries. Thus determinant is not zero.